Question

what is the following product?
\sqrt{30} \cdot \sqrt{10}
\bigcirc \\ 2\sqrt{10}
\bigcirc \\ 3\sqrt{10}
\bigcirc \\ 4\sqrt{10}
\bigcirc \\ 10\sqrt{3}

Explanation:

Step1: Use property of square roots

The property of square roots states that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ for non - negative real numbers $a$ and $b$. So, for $\sqrt{30}\cdot\sqrt{10}$, we have $\sqrt{30\times10}=\sqrt{300}$.

Step2: Simplify the square root

We can factorize $300$ as $100\times3$. Then $\sqrt{300}=\sqrt{100\times3}$. Since $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (for $a = 100$ and $b = 3$), we get $\sqrt{100}\cdot\sqrt{3}$. And $\sqrt{100} = 10$, so $\sqrt{100}\cdot\sqrt{3}=10\sqrt{3}$.

Answer:

D. $10\sqrt{3}$ (assuming the last option is D, as per the options given: $2\sqrt{10}$, $3\sqrt{10}$, $4\sqrt{10}$, $10\sqrt{3}$)